Two Cool Applets for 3D visualization

I recently stumbled across these two applets for helping students with 3D visualization. The first one gives you a 3D object, and you have to manipulate it so that you are viewing the appropriate side view. The second one is slightly more complex. In it you have to build a 3d object based on its top, front, and side views. This is a perfect example of what I like to see in a virtual manipulative: the content is truly interactive, it is much easier than doing the same thing with pencil and paper, and although it does have a component of repetitve practice it is in the context of student manipulated content. I would suggest using them in the following order:

1) Rotating 3D shapes to see a particular side view: http://www.fi.uu.nl/toepassingen/00247/toepassing_wisweb.en.html

2) Building 3D shapes based on side and top views: http://www.fi.uu.nl/toepassingen/02015/toepassing_wisweb.en.html

Project Interactivate

Project Interactivate is from Shodor Interactive, and contains a very large number of java applets for use in math education. The quality of the applets vary from very good and inventive, to fairly limited. Browsing the "Activities" as a learner will show you all of the 100+ applets available, while browsing "Lessons" as an instructor will list only the applets that have lessons included with them. http://www.shodor.org/interactivate/

National Library of Virtual Manipulatives

The National Library of Virtual Manipulatives is a a collection of math applets for k-12. The quality of the applets is very good and strengthened by the inclusion of structed lessons for many of them. The only limitation of the site is that while it does contain a large number of applets they don't go beyond the level of about Algebra I or early Geometry. Applets can be searched for by grade level and subject area, but you will soon find a lot of overlap between adjoining grade level areas. http://nlvm.usu.edu/en/nav/vlibrary.html

Geogebra Tutorial

As promised, here is a video tutorial of how to create a simple virtual manipulative in GeoGebra. You can watch the embedded video below, or follow the link to a higher quality version on my site.

Link to video: http://plaza.ufl.edu/youngdj/geogebra_tutorial/geogebra_tutorial.html (Full Quality 5Mb Flash movie)

Link to the java applet created in the tutorial: http://plaza.ufl.edu/youngdj/geogebra_tutorial/linegraph.html

Geogebra - The Future of Math Education

www.geogebra.org - Geogebra is completely free.

This is going to sound like a paid advertisement, but I can not begin to explain the brilliance of this program. It is so good on so many levels that it is unreal. I recently had the priveledge to attend a presentation by the author of this program, Markus Hohenwarter at the Florida Educational Technology Conference in Orlando and was blown away.

Geogebra is completely free.

Geogebra is very similar to Geometer's Sketchpad. Unfortunately, my comparison between the programs has to end there as financial restraints have prevented me from ever being very familiar with that program. I would very much like to hear a comparison of the two programs made by someone with a lot of experience with Geometer's Sketchpad. Essentially, Geogebra it is a program for creating interactive mathematical diagrams that also include all algebraic expressions. The scope of the program is very broad, covering almost all functions and digrams covered in high school Algebra, Geometry and Calculus (I say almost only because I haven't used the program long enough to know for sure if it is lacking in any content). Additionally, Geogebra provides features geared towards promoting interaction with content. For example, sliders can be easily placed on diagrams and assigned to values.

Geogebra is completely free.

As if the mere existence of such a free powerful program was not enough, the program has been created in java making it available for use on any platform. As such, Geogebra allows the user to output diagrams as stand-alone java applets. The power of this feature is groundbreaking (yes, I know it was available in Geometer's Skethpad, but not for free). What this means is that any teacher will be able to use the program to easily create customized virtual manipulatives and interactive worksheets for their classroom. Many teachers are already doing this and contributing their content to the Geogebra wiki and user forums (see www.geogebra.org for these and other geogebra resources). Virtual manipulatives that would take me 10-12 hours to create in Flash can literally be created in minutes by someone with no programming experience whatsoever.

Geogebra is completely free.

It is my hope to have some video tutorials for the program completed in the near future, and you will find them here when they are ready. For now you need to do 3 things. 1) Download the program and start using it. 2) Tell every math teacher you know about it. 3) Support the free mentality that the program was created on by posting your lessons to the Geogebra wiki for other teachers to use.

Did I mention that Geogebra is completely free?

Welcome & Rationale

Welcome to the Interactive Math blog. Here you will find resources for interactive math on the web. My goal is to provide links to the best interactive math sites (see next paragraph) on the web as well as provide information on how to create your own interactive math resources and how to best utilize them in the classroom. Please feel free to contribute links, ideas, and discussion through the use of the comments feature.

To begin with, I feel like I need to define what I mean by "the best interactive math sites". I am primarily refering to Virtual Manipulatives, which usually take the form of Java or Flash Applets. I will not provide links to resources that are not truly interactive. For example, pages that provide click-to-check practice will not be discussed here unless for verbal derision (see http://www.aaamath.com/). Additionally, the world has no shortage of static math textbooks and so static math webpages hold no interest for me (See http://www.purplemath.com/modules/index.htm). This may all sound very harsh, but I truly believe that if we are going to use the internet to educate math students we should be using the very best technologies that the web has to offer in order to provide learning experiences that students would have no other way of experiencing.

The examples listed above may be useful to some people in some cases and I don't mean to offend the people who have invested countless hours in creating them, but I believe they represent the past of internet-based math instruction. The future of internet-based math isntruction is all about student interaction with content for experiential learning through (computer-mediated) physical interaction and modeling. See the National Library of Virtual Manipulatives or Explore Learning (pay site) as positive examples of what I will be featuring on this blog.